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<h1 class="ltx_title ltx_title_section">Difference of averaging filters</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">The difference of averaging filters <cite class="ltx_cite">[<a href="#bib.bib15" title="Simultaneous multiple-emitter fitting for single molecule super-resolution imaging" class="ltx_ref">1</a>]</cite> is another type
of a band-pass filter. The filtered image is obtained by subtracting
images filtered with two <a href="BoxFilterUI.html" title="" class="ltx_ref">averaging filters</a>
having different user-specified kernel sizes,</p>
<table id="Sx1.Ex1" class="ltx_equation">

<tr class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi46.png" width="206" height="18" alt="F=I*K_{\mathrm{AV1}}-I*K_{\mathrm{AV2}}\,."></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">Similar to the <a href="DifferenceOfGaussiansFilterUI.html" title="" class="ltx_ref">difference-of-Gaussians filter</a>,
the size of the kernel <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi48.png" width="46" height="18" alt="K_{\mathrm{AV2}}"> has to be larger than <img id="Sx1.p1.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi47.png" width="46" height="18" alt="K_{\mathrm{AV1}}">.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">Threshold for approximate localization of molecules</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<p class="ltx_p">The <a href="../../detectors/Threshold.html" title="" class="ltx_ref">threshold</a> value can be
specified by users as an expression combining mathematical functions
and operators with variables based on the current raw or filtered
image. Variables provided by this filter are:</p>
</div>
<div id="Sx1.SSx1.p2" class="ltx_para">
<table class="ltx_tabular ltx_align_middle">
<thead class="ltx_thead">
<tr class="ltx_tr">
<th class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">DoB.I</span></th>
<th class="ltx_td ltx_align_left">current raw input image</th>
</tr>
<tr class="ltx_tr">
<th class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">DoB.F</span></th>
<th class="ltx_td ltx_align_left">corresponding filtered image</th>
</tr>
</thead>
<tbody class="ltx_tbody">
<tr class="ltx_tr">
<th class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">DoB.B1</span></th>
<td class="ltx_td ltx_align_left">result of filtering only with <img id="Sx1.SSx1.p2.m1" class="ltx_Math" style="vertical-align:-5px" src="mi/mi47.png" width="46" height="18" alt="K_{\mathrm{AV1}}">
</td>
</tr>
<tr class="ltx_tr">
<th class="ltx_td ltx_align_left"><span class="ltx_text ltx_font_typewriter">DoB.B2</span></th>
<td class="ltx_td ltx_align_left">result of filtering only with <img id="Sx1.SSx1.p2.m2" class="ltx_Math" style="vertical-align:-5px" src="mi/mi48.png" width="46" height="18" alt="K_{\mathrm{AV2}}">
</td>
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</tbody>
</table>
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<div id="Sx1.SSx2" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx2.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Filters.html" title="" class="ltx_ref">Image filtering and feature enhancement</a></p>
</div>
</li>
<li id="I1.i2" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i2.p1" class="ltx_para">
<p class="ltx_p"><a href="../../detectors/Detectors.html" title="" class="ltx_ref">Finding approximate positions of molecules</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib15" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">F. Huang, S. L. Schwartz, J. M. Byars and K. A. Lidke</span><span class="ltx_text ltx_bib_year">(2011)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Simultaneous multiple-emitter fitting for single molecule super-resolution imaging</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Biomedical Optics Express</span> <span class="ltx_text ltx_bib_volume">2</span> (<span class="ltx_text ltx_bib_number">5</span>), <span class="ltx_text ltx_bib_pages"> pp. 1377–93</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1364/BOE.2.001377" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Difference of averaging filters" class="ltx_ref"><span class="ltx_text ltx_ref_title">Difference of averaging filters</span></a>.
</span>
</li>
</ul>
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